Let E be a Galois extension of ? of degree l, not necessarily solvable. In this paper we first prove that the L-function L(s, π) attached to an automorphic cuspidal representation π of $ GL_m (E_\mathbb{A} ) $ canno...Let E be a Galois extension of ? of degree l, not necessarily solvable. In this paper we first prove that the L-function L(s, π) attached to an automorphic cuspidal representation π of $ GL_m (E_\mathbb{A} ) $ cannot be factored nontrivially into a product of L-functions over E.Next, we compare the n-level correlation of normalized nontrivial zeros of L(s, π1)…L(s, π k ), where π j , j = 1,…, k, are automorphic cuspidal representations of $ GL_{m_j } (\mathbb{Q}_\mathbb{A} ) $ , with that of L(s,π). We prove a necessary condition for L(s, π) having a factorization into a product of L-functions attached to automorphic cuspidal representations of specific $ GL_{m_j } (\mathbb{Q}_\mathbb{A} ) $ , j = 1,…,k. In particular, if π is not invariant under the action of any nontrivial σ ∈ Gal E/?, then L(s, π) must equal a single L-function attached to a cuspidal representation of $ GL_{m\ell } (\mathbb{Q}_\mathbb{A} ) $ and π has an automorphic induction, provided L(s, π) can factored into a product of L-functions over ?. As E is not assumed to be solvable over ?, our results are beyond the scope of the current theory of base change and automorphic induction.Our results are unconditional when m,m 1,…,m k are small, but are under Hypothesis H and a bound toward the Ramanujan conjecture in other cases.展开更多
We compute the n-level correlation of normalized nontrivial zeros of a product of Lfunctions:L(s,π1)…L(s,πk),whereπj,j=1,…,k,are automorphic cuspidal representations of GL mj(?A).Here the sizes of the groups GL m...We compute the n-level correlation of normalized nontrivial zeros of a product of Lfunctions:L(s,π1)…L(s,πk),whereπj,j=1,…,k,are automorphic cuspidal representations of GL mj(?A).Here the sizes of the groups GL mj(?A)are not necessarily the same.When these L(s,πj)are distinct,we prove that their nontrivial zeros are uncorrelated,as predicted by random matrix theory and verified numerically.When L(s,πj)are not necessarily distinct,our results will lead to a proof that the n-level correlation of normalized nontrivial zeros of the product L-function follows the superposition of Gaussian Unitary Ensemble(GUE)models of individual L-functions and products of lower rank GUEs.The results are unconditional when m 1,…,m k?4,but are under Hypothesis H in other cases.展开更多
Let πr be an irreducible unitary cuspidal representation of GL,^（AQ）, m ≥ 2. Assume that π is self-contragredient. The author gets upper and lower bounds of the same order for fractional moments of automorphic L-...Let πr be an irreducible unitary cuspidal representation of GL,^（AQ）, m ≥ 2. Assume that π is self-contragredient. The author gets upper and lower bounds of the same order for fractional moments of automorphic L-function L（s, π） on the critical line under Generalized Ramanujan Conjecture; the upper bound being conditionally subject to the truth of Generalized Riemann Hypothesis.展开更多
Let π be an irreducible unitary cuspidal representation of GLm（AQ） with m ≥ 2, and L（s, Tr） the L-function attached to π. Under the Generalized Riemann Hypothesis for L（s,π）, we estimate the normal density o...Let π be an irreducible unitary cuspidal representation of GLm（AQ） with m ≥ 2, and L（s, Tr） the L-function attached to π. Under the Generalized Riemann Hypothesis for L（s,π）, we estimate the normal density of primes in short intervals for the automorphic L-function L（s, π）. Our result generalizes the corresponding theorem of Selberg for the Riemann zeta-function.展开更多
In this paper we prove zero-density estimates of the large sieve type for the automorphic L-function L（s, f × χ）, where f is a holomorphic cusp form and χ（mod q） is a primitive character.
Let f be a holomorphic Hecke cusp form with even integral weight k≥2 for the full modular group,and letχbe a primitive Dirichlet character modulo q.Let Lf(s,χ)be the automorphic L-function attached to f andχ-We st...Let f be a holomorphic Hecke cusp form with even integral weight k≥2 for the full modular group,and letχbe a primitive Dirichlet character modulo q.Let Lf(s,χ)be the automorphic L-function attached to f andχ-We study the mean-square estimate of Lf(s,χ)and establish an asymptotic formula.展开更多
In this paper,the existence,uniqueness,asymptotic and global exponential stability of pseudo almost automorphic solution for a class of delayed Lasota-Wazewska model with impulsive effects are established by applying ...In this paper,the existence,uniqueness,asymptotic and global exponential stability of pseudo almost automorphic solution for a class of delayed Lasota-Wazewska model with impulsive effects are established by applying an appropriate fixed point theorem and Lyapunov functional method.Finally,a numerical example with simulation is given to illuminate our theoretical results.展开更多
Let π and π' be automorphic irreducible cuspidal representations of GLm(QA) and GLm'(QA),respectively,and L(s,π×■) be the Rankin-Selberg L-function attached to π and π'.Without assuming the Gene...Let π and π' be automorphic irreducible cuspidal representations of GLm(QA) and GLm'(QA),respectively,and L(s,π×■) be the Rankin-Selberg L-function attached to π and π'.Without assuming the Generalized Ramanujan Conjecture(GRC),the author gives the generalized prime number theorem for L(s,π×■) when π≌π'.The result generalizes the corresponding result of Liu and Ye in 2007.展开更多
In this paper we discuss the existence and global attractivity of k-almost automorphic sequence solution of a model of cellular neural networks. We consider the corresponding difference equation analogue of the model ...In this paper we discuss the existence and global attractivity of k-almost automorphic sequence solution of a model of cellular neural networks. We consider the corresponding difference equation analogue of the model system using suitable discretization method and obtain certain conditions for the existence of solution. Almost automorphic function is a good generalization of almost periodic function. This is the first paper considering such solutions of the neural networks.展开更多
For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-al...For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-almost automorphic functions, we give sufficient conditions of the existence and uniqueness of almost automorphic solutions of a differential equation with a piecewise constant argument of generalized type. This is done using the Banach fixed point theorem.展开更多
The Khuri-Jones correction to the partial wave scattering amplitude at threshold is an automorphic function for a dihedron. An expression for the partial wave amplitude is obtained at the pole which the upper half-pla...The Khuri-Jones correction to the partial wave scattering amplitude at threshold is an automorphic function for a dihedron. An expression for the partial wave amplitude is obtained at the pole which the upper half-plane maps on to the interior of semi-infinite strip. The Lehmann ellipse exists below threshold for bound states. As the system goes from below to above threshold, the discrete dihedral (elliptic) group of Type 1 transforms into a Type 3 group, whose loxodromic elements leave the fixed points 0 and ∞ invariant. The transformation of the indifferent fixed points from -1 and +1 to the source-sink fixed points 0 and ∞ is the result of a finite resonance width in the imaginary component of the angular momentum. The change in symmetry of the groups, and consequently their tessellations, can be used to distinguish bound states from resonances.展开更多
Letλ_(f×f)(n)be the nth Fourier coeficient of Rankin-Selberg L-function L(f×f,s).In this paper,we are interested in the average behavior of coeficients of Rankin-Selberg L-functions over sparse sequences,an...Letλ_(f×f)(n)be the nth Fourier coeficient of Rankin-Selberg L-function L(f×f,s).In this paper,we are interested in the average behavior of coeficients of Rankin-Selberg L-functions over sparse sequences,and establish the asymptotic formula ofΣ_(n≤xλ_(f×f)n^(m)).展开更多
In this paper, we establish asymptotic formulas for a cubic moment of Dirichlet L-functions restricted to a coset, as well as for a mixed moment of Dirichlet L-functions and twists of GL(2) L-functions along a coset. ...In this paper, we establish asymptotic formulas for a cubic moment of Dirichlet L-functions restricted to a coset, as well as for a mixed moment of Dirichlet L-functions and twists of GL(2) L-functions along a coset. Our main tool is a power-saving estimate of bilinear forms of hyper-Kloosterman sums due to Kowalski–Michel–Sawin.展开更多
Suppose F is a field of characteristic not 2 and F* its multiplicative group. Let T*n(F) be the multiplicative group of invertible upper triangular n x n matrices over F and STn(F) its subgroup {(aij) E T*n(F)aii = 1,...Suppose F is a field of characteristic not 2 and F* its multiplicative group. Let T*n(F) be the multiplicative group of invertible upper triangular n x n matrices over F and STn(F) its subgroup {(aij) E T*n(F)aii = 1, i}. This paper proves that f: T*n(F) → T*n(F) is a group automorphism if and only if there exist a matrix Q in T*n(F) and a field automorphism rs of F such that either where A = ((aij)), A-T is the transpose inverse of A, J = Ei n+1-i, and : i= 1T*n(F) → F* is a homomorphism which satisfies {(xIn)(x)x F*} = F* and {x F*(xIn)(x) = 1} = {1}. Simultaneously, they also determine the automorphisms of STn(F).展开更多
Recall that a subgroup H of a finite group G is called a TI-subgroup if H ∩ H^9 = 1 or H for each g ∈ G. Suppose that G is a finite group whose second maximal subgroups are TI-subgroups. It is shown that every class...Recall that a subgroup H of a finite group G is called a TI-subgroup if H ∩ H^9 = 1 or H for each g ∈ G. Suppose that G is a finite group whose second maximal subgroups are TI-subgroups. It is shown that every class-preserving Coleman automorphism of G is an inner automorphism. As an immediate consequence of this result, we obtain that the normalizer property holds for G.展开更多
Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ ： G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h（p）,...Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ ： G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h（p）, where h（p） is a function depending only on p. In particular, if α^3 = 1, then the nilpotent class of G is at most 2.展开更多
Let G be a primitive group. It is proved that there exits some prime p such that every p-central automorphism of G is inner. As an application, it is proved that every Coleman automorphism of the holomorph of G is inn...Let G be a primitive group. It is proved that there exits some prime p such that every p-central automorphism of G is inner. As an application, it is proved that every Coleman automorphism of the holomorph of G is inner. In particular, the normalizer property holds for such groups in question. Additionally, other related results are obtained as well.展开更多
In this paper, we determine the order of automorphism group of p-groups in the third family ( Φ 3) and the fourth family ( Φ 4) in [1], whose order is p^6(p≥3). Here p denotes an odd prime.
In this paper by techniques of group we give some formulae for solving the general quadratic equations of two variables over a finite field,completely calculate and uniformly deal with the orders of automorphism group...In this paper by techniques of group we give some formulae for solving the general quadratic equations of two variables over a finite field,completely calculate and uniformly deal with the orders of automorphism groups of all p-groups of orders less than p6 under the P Hall's concept of isoclinism,also make a number of corrections for orders of automorphism groups offered for a mistake or fault before.展开更多
基金supported by the National Basic Research Program of China, the National Natural Science Foundation of China (Grant No. 10531060)Ministry of Education of China (Grant No. 305009)+1 种基金The second author was supported by the National Security Agency (Grant No. H98230-06-1-0075)The United States Government is authorized to reproduce and distribute reprints notwithstanding any copyright notation herein
文摘Let E be a Galois extension of ? of degree l, not necessarily solvable. In this paper we first prove that the L-function L(s, π) attached to an automorphic cuspidal representation π of $ GL_m (E_\mathbb{A} ) $ cannot be factored nontrivially into a product of L-functions over E.Next, we compare the n-level correlation of normalized nontrivial zeros of L(s, π1)…L(s, π k ), where π j , j = 1,…, k, are automorphic cuspidal representations of $ GL_{m_j } (\mathbb{Q}_\mathbb{A} ) $ , with that of L(s,π). We prove a necessary condition for L(s, π) having a factorization into a product of L-functions attached to automorphic cuspidal representations of specific $ GL_{m_j } (\mathbb{Q}_\mathbb{A} ) $ , j = 1,…,k. In particular, if π is not invariant under the action of any nontrivial σ ∈ Gal E/?, then L(s, π) must equal a single L-function attached to a cuspidal representation of $ GL_{m\ell } (\mathbb{Q}_\mathbb{A} ) $ and π has an automorphic induction, provided L(s, π) can factored into a product of L-functions over ?. As E is not assumed to be solvable over ?, our results are beyond the scope of the current theory of base change and automorphic induction.Our results are unconditional when m,m 1,…,m k are small, but are under Hypothesis H and a bound toward the Ramanujan conjecture in other cases.
基金supported by the 973 Programthe National Natural Science Foundation of China(GrantNo.10531060)+2 种基金Ministry of Education of China(Grant No.305009)The second author was supportedby the National Security Agency of USA(Grant No.H98230-06-1-0075)The United States government isauthorized to reproduce and distribute reprints notwithstanding any copyright notation herein.
文摘We compute the n-level correlation of normalized nontrivial zeros of a product of Lfunctions:L(s,π1)…L(s,πk),whereπj,j=1,…,k,are automorphic cuspidal representations of GL mj(?A).Here the sizes of the groups GL mj(?A)are not necessarily the same.When these L(s,πj)are distinct,we prove that their nontrivial zeros are uncorrelated,as predicted by random matrix theory and verified numerically.When L(s,πj)are not necessarily distinct,our results will lead to a proof that the n-level correlation of normalized nontrivial zeros of the product L-function follows the superposition of Gaussian Unitary Ensemble(GUE)models of individual L-functions and products of lower rank GUEs.The results are unconditional when m 1,…,m k?4,but are under Hypothesis H in other cases.
基金Project supported by the National Natural Science Foundation of China (No. 10971119)
文摘Let πr be an irreducible unitary cuspidal representation of GL,^（AQ）, m ≥ 2. Assume that π is self-contragredient. The author gets upper and lower bounds of the same order for fractional moments of automorphic L-function L（s, π） on the critical line under Generalized Ramanujan Conjecture; the upper bound being conditionally subject to the truth of Generalized Riemann Hypothesis.
基金Supported by NSFC Grant #10531060by a Ministry of Education Major Grant Program in Sciences and Technology
文摘Let π be an irreducible unitary cuspidal representation of GLm（AQ） with m ≥ 2, and L（s, Tr） the L-function attached to π. Under the Generalized Riemann Hypothesis for L（s,π）, we estimate the normal density of primes in short intervals for the automorphic L-function L（s, π）. Our result generalizes the corresponding theorem of Selberg for the Riemann zeta-function.
基金Mathematical Tianyuan Foundation(No.10826028)National Natural Science Foundation of China(Grant No.10771127,10571107)
文摘In this paper we prove zero-density estimates of the large sieve type for the automorphic L-function L（s, f × χ）, where f is a holomorphic cusp form and χ（mod q） is a primitive character.
基金the National Natural Science Foundation of China(Grant No.11601309).
文摘Let f be a holomorphic Hecke cusp form with even integral weight k≥2 for the full modular group,and letχbe a primitive Dirichlet character modulo q.Let Lf(s,χ)be the automorphic L-function attached to f andχ-We study the mean-square estimate of Lf(s,χ)and establish an asymptotic formula.
文摘In this paper,the existence,uniqueness,asymptotic and global exponential stability of pseudo almost automorphic solution for a class of delayed Lasota-Wazewska model with impulsive effects are established by applying an appropriate fixed point theorem and Lyapunov functional method.Finally,a numerical example with simulation is given to illuminate our theoretical results.
文摘Let π and π' be automorphic irreducible cuspidal representations of GLm(QA) and GLm'(QA),respectively,and L(s,π×■) be the Rankin-Selberg L-function attached to π and π'.Without assuming the Generalized Ramanujan Conjecture(GRC),the author gives the generalized prime number theorem for L(s,π×■) when π≌π'.The result generalizes the corresponding result of Liu and Ye in 2007.
基金supported by the National Natural Science Foundation of China (10901140, 11171090)ZJNSFC (Y6100029, Y6100696, Y6110195)
文摘In this paper we discuss the existence and global attractivity of k-almost automorphic sequence solution of a model of cellular neural networks. We consider the corresponding difference equation analogue of the model system using suitable discretization method and obtain certain conditions for the existence of solution. Almost automorphic function is a good generalization of almost periodic function. This is the first paper considering such solutions of the neural networks.
文摘For a set S of real numbers, we introduce the concept of S-almost automorphic functions valued in a Banach space. It generalizes in particular the space of Z-almost automorphic functions. Considering the space of S-almost automorphic functions, we give sufficient conditions of the existence and uniqueness of almost automorphic solutions of a differential equation with a piecewise constant argument of generalized type. This is done using the Banach fixed point theorem.
文摘The Khuri-Jones correction to the partial wave scattering amplitude at threshold is an automorphic function for a dihedron. An expression for the partial wave amplitude is obtained at the pole which the upper half-plane maps on to the interior of semi-infinite strip. The Lehmann ellipse exists below threshold for bound states. As the system goes from below to above threshold, the discrete dihedral (elliptic) group of Type 1 transforms into a Type 3 group, whose loxodromic elements leave the fixed points 0 and ∞ invariant. The transformation of the indifferent fixed points from -1 and +1 to the source-sink fixed points 0 and ∞ is the result of a finite resonance width in the imaginary component of the angular momentum. The change in symmetry of the groups, and consequently their tessellations, can be used to distinguish bound states from resonances.
基金Supported by Natural Science Foundation of Shandong Province(No.ZR2024MA053)。
文摘Letλ_(f×f)(n)be the nth Fourier coeficient of Rankin-Selberg L-function L(f×f,s).In this paper,we are interested in the average behavior of coeficients of Rankin-Selberg L-functions over sparse sequences,and establish the asymptotic formula ofΣ_(n≤xλ_(f×f)n^(m)).
基金Supported by the National Key R&D Program of China(Grant No.2021YFA1000700)National Natural Science Foundation of China(Grant No.12031008)。
文摘In this paper, we establish asymptotic formulas for a cubic moment of Dirichlet L-functions restricted to a coset, as well as for a mixed moment of Dirichlet L-functions and twists of GL(2) L-functions along a coset. Our main tool is a power-saving estimate of bilinear forms of hyper-Kloosterman sums due to Kowalski–Michel–Sawin.
基金This work is supported by NSF of China NSF of Heilongjiang province
文摘Suppose F is a field of characteristic not 2 and F* its multiplicative group. Let T*n(F) be the multiplicative group of invertible upper triangular n x n matrices over F and STn(F) its subgroup {(aij) E T*n(F)aii = 1, i}. This paper proves that f: T*n(F) → T*n(F) is a group automorphism if and only if there exist a matrix Q in T*n(F) and a field automorphism rs of F such that either where A = ((aij)), A-T is the transpose inverse of A, J = Ei n+1-i, and : i= 1T*n(F) → F* is a homomorphism which satisfies {(xIn)(x)x F*} = F* and {x F*(xIn)(x) = 1} = {1}. Simultaneously, they also determine the automorphisms of STn(F).
基金Supported by the National Natural Science Foundation of China(Grant Nos.1117116911071155)the Doc-toral Foundation of Shandong Province(Grant No.BS2012SF003)
文摘Recall that a subgroup H of a finite group G is called a TI-subgroup if H ∩ H^9 = 1 or H for each g ∈ G. Suppose that G is a finite group whose second maximal subgroups are TI-subgroups. It is shown that every class-preserving Coleman automorphism of G is an inner automorphism. As an immediate consequence of this result, we obtain that the normalizer property holds for G.
基金The NSF(11371124)of Chinathe NSF(F2015402033)of Hebei Provincethe Doctoral Special Foundation(20120066)of Hebei University of Engineering
文摘Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ ： G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h（p）, where h（p） is a function depending only on p. In particular, if α^3 = 1, then the nilpotent class of G is at most 2.
基金Supported by the National Natural Science Foundation of China(Grant No.71571108)Projects of International(Regional)Cooperation and Exchanges of NSFC(Grant Nos.71611530712+4 种基金 61661136002)Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20133706110002)Natural Science Foundation of Shandong Province(Grant No.ZR2015GZ007)Project Funded by China Postdoctoral Science Foundation(Grant No.2016M590613)the Specialized Fund for the Postdoctoral Innovative Research Program of Shandong Province(Grant No.201602035)
文摘Let G be a primitive group. It is proved that there exits some prime p such that every p-central automorphism of G is inner. As an application, it is proved that every Coleman automorphism of the holomorph of G is inner. In particular, the normalizer property holds for such groups in question. Additionally, other related results are obtained as well.
文摘In this paper, we determine the order of automorphism group of p-groups in the third family ( Φ 3) and the fourth family ( Φ 4) in [1], whose order is p^6(p≥3). Here p denotes an odd prime.
基金Supported by the National Natural Science Foundation of China(61074185)Supported by the Projection of Science and Technique for Guangdong Province(2009B030802044)+1 种基金Supported by the Projection of Production,Study and Investigation for Guangdong Province(2010B090301042)Supported by the Science and Study Foundation of Guangxi University(XB2100285)
文摘In this paper by techniques of group we give some formulae for solving the general quadratic equations of two variables over a finite field,completely calculate and uniformly deal with the orders of automorphism groups of all p-groups of orders less than p6 under the P Hall's concept of isoclinism,also make a number of corrections for orders of automorphism groups offered for a mistake or fault before.
